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# System prepended metadata

title: Econ2 HW4

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# Econ2 HW4
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1.
( a )
The inputs used to produce goods and services
( b )
The marginal product of an input times the price of the output
2.
( a )
The milk market is perfect competitive to the firm since the it is a price taker.
( b )
The robot renting market is also perfectly competitive since the Smiling Cow Dairy is a price taker.
( c )
| Number of Robots | Marginal Product(gallons) | Value of Marginal Product($) |
| --- | --- | --- |
|   1 |  50 | 200 |
|   2 |  35 | 140 |
|   3 |  30 | 120 |
|   4 |  25 | 100 |
|   5 |  10 |  40 |
|   6 |   5 |  20 |

( d )
The firm should rent 4 robots because the value of marginal products of the first 4 robots are greater than the marginal costs(rental price $100).
3.
( a )
$Wage=ValueOfMarginalProduct=2\times(100-2L)=200-4L$
$L_{orchard}=50-\frac{Wage}4$
$L_{market}=L_{orchard}\times20=1000-5\times Wage$
( b )
$Wage=200-\frac{L_{market}}5=160$
Each firm hires $\frac{200}{20}=10\ labors$
$Q=100\times10-(10)^2=900\ apples$
$Profit=900\times2-160\times10=200$
( c )
$Wage'=4\times (100-2L)=400-8\times(\frac{200}{20})=320$
$Q'=100\times10-(10)^2=900\ apples$
$Profit=900\times4-320\times10=400$
Income of workers and orchard owners' both double as the price doubles.
( d )
$Wgae''=200-4\times \frac{200}{10}=120$
$Q=100\times 20-(20)^2=1600$
$Profit=1600\times 2-120\times 20=800$
$OriginalTotalIncome=200\times 20+160\times 200=36000$
$NewTotalIncome=800\times 10+120\times 200=32000$
The total income of the nation goes down.
4.
The value of the marginal product of the last worker is $12/hour.
The last worker produces $\frac{12}6=2$ sandwitches per hour
5.
( a )
Hire the amount of workers such that the value of marginal product is equal to the wage rate.
( b )
$\frac{150}{30}=5$
( c )
Labor market
![](https://i.imgur.com/kMDx2gv.png =40%x)
Demand
![](https://i.imgur.com/vJMEhIS.png =30%x)
The equilibrium wage is determined by the supply and demand of labor. Each firm than use the market wage and their demand to set their quantity of employment.
( d )
Labor market
![](https://i.imgur.com/GNMFVBj.png =40%x)
Demand
![](https://i.imgur.com/sLqUfHl.png =30%x)
Labor supply shifts to the left, causing equilibrium wage to rise. The marginal product of labor rises as the wage rises.